The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I

Abstract

Given an open book decomposition (S,h) adapted to a closed, oriented 3-manifold M, we define a chain map from a certain Heegaard Floer chain complex associated to (S,h) to a certain embedded contact homology chain complex associated to (S,h), as defined in arXiv:1008.2734, and prove that it induces an isomorphism on the level of homology. This implies the isomorphism between the hat version of Heegaard Floer homology of -M and the hat version of embedded contact homology of M.

161 pages, 6 figures. Second version: exposition improvements, index of notation, more details about degenerations of J-holomorphic curves

Cited by in corpus (5)

• A contact invariant in sutured monopole homology
• A splitting theorem for the Seiberg-Witten invariant of a homology $S^1\times S^3$
• On the monopole Lefschetz number of finite order diffeomorphisms
• On the equivalence of contact invariants in sutured Floer homology theories
• Dimensionally-reduced sutured Floer homology as a string homology